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The following are marks scored by form four student in Mathematics test.

Marks10-1920-2930-3940-4950-5960-6970-7980-8990-99
Frequency 2 6 10 16 24 20 12 8 2

Using an assumed mean of 54.5, calculate the

  1. Mean mark 
  2. Variance 
  3. Standard deviation 

1 Answer

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  1. Mean mark 
    MarksMp(x)d(x-a)FdD2Fd2 
    10-19214.5-40-801600 3200 
    20-29624.5-30-1809005400
    30-391034.5-20-2004004000
    40-491644.5-10-1601001600
    50-592454.50000
    60-692064.510200100200
    70-791274.5202404004800
    80-89884.5302409007200
    90-99294.5408016003200
        140 31400
  2. Mean = A + Σfd
                    Σf
    = 54.5 + 140/100 = 55.9
  3. Variance 
    Variance= 31400/100 – (140/100)2
    = 312.04
  4. Standard deviation 
    standard variation = √variance
    √ 312.04 = 17.06
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